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150.
I did it with a combination of some unconventional logic and brute force..but did it in less than 2 min..wud like to know any other sophisticated method

Oh god..
Actually, AP, GP are not in the syllabus of GMAT..so i forget about them and tend not to use them.
But yes, if one can apply them..one shud do that.At the end of the day, nobody is going to know how u arrived at right answer.

999 is the highest in value for 3 digit numbers. Divide it with 6 and take the integer part ONLY to get the total number of numbers divisible by 6.
=> 999/6 = 166
However, it does include numbers up to 100 which we donot need.
=> 100/6 = 16

So, the required number of 3 digit numbers = 166-16 = 150.

As per my understanding 3 digit numbers are from 100 to 999.

If I were to take your suggestion, I can never define the number of digits at all. Say,
1 - one digit
01 - two digits
001 - three digits
0001 - four digits
.
.
.
.
.

This can go on and on and on. In essense, all the above numbers represent the single digit 1, though.

Any other opinions on the query raised by 'amernassar'.

amernassar wrote:

150 is not accurate.

The 3 digit number includes also 006,012,..... . No mention in the text that the hundreth digit is not a 0 digit.

A number is divisible by 6 if it is divisble by both 2 and 3

Numbers divisible by 2 = multiple of 2, 2,4,6...
Numbers divisible by 3 = multiple of 3, 3,6,9,...

So the number number be a multiple of 6 (LCM)

From 100-999, there are 900 numbrs. Numbers divisible by 6 = 900/6 = 150
(Because for every group of 6 numbers starting from 100, only 1 is divisible by 6)

I understand your point. Good example on locker code.

But, in general, when thay say a "two digit number", that means 10x+y where x <> 0. Example: 11, 23, 99. Not 09 or 01.

You can think of zero as a valid digit in the front of the number (say, 09) only when you consider that as a text. When you consider that as a number, it is a single digit (9). (My sybase knowledge comes handy atlast )

You may corelate this with typing a number in MS excel with property defined as text and number.